{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NZSOV4C44O2HZMB7VQWLOSNH45","short_pith_number":"pith:NZSOV4C4","canonical_record":{"source":{"id":"1803.05379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-14T16:16:03Z","cross_cats_sorted":["math.FA","math.MP","quant-ph"],"title_canon_sha256":"ab1489b28e482a8d5e635c186b63e4da25b43eadf86bd7e1cd1b3c31e1514975","abstract_canon_sha256":"e22d91c865c3bd75c72bacceaf64770c4ab385474d38e4df22a13410bbea8102"},"schema_version":"1.0"},"canonical_sha256":"6e64eaf05ce3b47cb03fac2cb749a7e75bd4df729baa74ec57cc3b6836ba11b2","source":{"kind":"arxiv","id":"1803.05379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05379","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05379v3","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05379","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"NZSOV4C44O2H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NZSOV4C44O2HZMB7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NZSOV4C4","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NZSOV4C44O2HZMB7VQWLOSNH45","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-14T16:16:03Z","cross_cats_sorted":["math.FA","math.MP","quant-ph"],"title_canon_sha256":"ab1489b28e482a8d5e635c186b63e4da25b43eadf86bd7e1cd1b3c31e1514975","abstract_canon_sha256":"e22d91c865c3bd75c72bacceaf64770c4ab385474d38e4df22a13410bbea8102"},"schema_version":"1.0"},"canonical_sha256":"6e64eaf05ce3b47cb03fac2cb749a7e75bd4df729baa74ec57cc3b6836ba11b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:54.433964Z","signature_b64":"G4ScMxEvenMFu2XoCpNLKGyANbLNoNTLQubtYQj5IpPcXIEn4K77parzjjl5aYZVcJQAXNAdGzfRYYJmjZHdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e64eaf05ce3b47cb03fac2cb749a7e75bd4df729baa74ec57cc3b6836ba11b2","last_reissued_at":"2026-05-18T00:10:54.433265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:54.433265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7PorqFCBY3pdElnrrFQj/DAMeL17DdsazpBRs2qkgLl6Jl0tCv8akXVdrgJnj922Wy9PofjxSkJw95wz0G3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:31:07.750939Z"},"content_sha256":"58f2e1bbb977257764588a9fa3f143b05e1176cbcb265bc4a0bfa5e288e267fb","schema_version":"1.0","event_id":"sha256:58f2e1bbb977257764588a9fa3f143b05e1176cbcb265bc4a0bfa5e288e267fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NZSOV4C44O2HZMB7VQWLOSNH45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypercontractivity and logarithmic Sobolev Inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Cambyse Rouz\\'e, Ivan Bardet","submitted_at":"2018-03-14T16:16:03Z","abstract_excerpt":"We generalize the concepts of weak quantum logarithmic Sobolev inequality (LSI) and weak hypercontractivity (HC), introduced in the quantum setting by Olkiewicz and Zegarlinski, to the case of non-primitive quantum Markov semigroups (QMS). The originality of this work resides in that this new notion of hypercontractivity is given in terms of the so-called amalgamated $\\mathbb{L}_p$ norms introduced recently by Junge and Parcet in the context of operator spaces theory. We make three main contributions. The first one is a version of Gross' integration lemma: we prove that (weak) HC implies (weak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05379","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrSdACYHQiN5vtsFgkqXFGtnh+MGD7hbsoaCPaamSTNOCzV0O+40veGt8yQ0IXHAFQMp7e24AorGyPoEi3lMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:31:07.751612Z"},"content_sha256":"0a9042415a21f3ffaacac4419daa06108a289085d30b2b03bf88402abfa2758b","schema_version":"1.0","event_id":"sha256:0a9042415a21f3ffaacac4419daa06108a289085d30b2b03bf88402abfa2758b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZSOV4C44O2HZMB7VQWLOSNH45/bundle.json","state_url":"https://pith.science/pith/NZSOV4C44O2HZMB7VQWLOSNH45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZSOV4C44O2HZMB7VQWLOSNH45/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T23:31:07Z","links":{"resolver":"https://pith.science/pith/NZSOV4C44O2HZMB7VQWLOSNH45","bundle":"https://pith.science/pith/NZSOV4C44O2HZMB7VQWLOSNH45/bundle.json","state":"https://pith.science/pith/NZSOV4C44O2HZMB7VQWLOSNH45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZSOV4C44O2HZMB7VQWLOSNH45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NZSOV4C44O2HZMB7VQWLOSNH45","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e22d91c865c3bd75c72bacceaf64770c4ab385474d38e4df22a13410bbea8102","cross_cats_sorted":["math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-14T16:16:03Z","title_canon_sha256":"ab1489b28e482a8d5e635c186b63e4da25b43eadf86bd7e1cd1b3c31e1514975"},"schema_version":"1.0","source":{"id":"1803.05379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05379","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05379v3","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05379","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"NZSOV4C44O2H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NZSOV4C44O2HZMB7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NZSOV4C4","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:0a9042415a21f3ffaacac4419daa06108a289085d30b2b03bf88402abfa2758b","target":"graph","created_at":"2026-05-18T00:10:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We generalize the concepts of weak quantum logarithmic Sobolev inequality (LSI) and weak hypercontractivity (HC), introduced in the quantum setting by Olkiewicz and Zegarlinski, to the case of non-primitive quantum Markov semigroups (QMS). The originality of this work resides in that this new notion of hypercontractivity is given in terms of the so-called amalgamated $\\mathbb{L}_p$ norms introduced recently by Junge and Parcet in the context of operator spaces theory. We make three main contributions. The first one is a version of Gross' integration lemma: we prove that (weak) HC implies (weak","authors_text":"Cambyse Rouz\\'e, Ivan Bardet","cross_cats":["math.FA","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-14T16:16:03Z","title":"Hypercontractivity and logarithmic Sobolev Inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05379","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:58f2e1bbb977257764588a9fa3f143b05e1176cbcb265bc4a0bfa5e288e267fb","target":"record","created_at":"2026-05-18T00:10:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e22d91c865c3bd75c72bacceaf64770c4ab385474d38e4df22a13410bbea8102","cross_cats_sorted":["math.FA","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-14T16:16:03Z","title_canon_sha256":"ab1489b28e482a8d5e635c186b63e4da25b43eadf86bd7e1cd1b3c31e1514975"},"schema_version":"1.0","source":{"id":"1803.05379","kind":"arxiv","version":3}},"canonical_sha256":"6e64eaf05ce3b47cb03fac2cb749a7e75bd4df729baa74ec57cc3b6836ba11b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e64eaf05ce3b47cb03fac2cb749a7e75bd4df729baa74ec57cc3b6836ba11b2","first_computed_at":"2026-05-18T00:10:54.433265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:54.433265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4ScMxEvenMFu2XoCpNLKGyANbLNoNTLQubtYQj5IpPcXIEn4K77parzjjl5aYZVcJQAXNAdGzfRYYJmjZHdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:54.433964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58f2e1bbb977257764588a9fa3f143b05e1176cbcb265bc4a0bfa5e288e267fb","sha256:0a9042415a21f3ffaacac4419daa06108a289085d30b2b03bf88402abfa2758b"],"state_sha256":"883533d294f7d63e228bcb688ab78459487b671a75386c2a9d1a15d9de322121"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SaUXU4iAYOl8dLtxdbNDCwuwWRTqQYC6vUPpOVKY2zwBsFB2joWIz9DQDje/FNAneW3yzL20G0mc+21O3Rg2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:31:07.755483Z","bundle_sha256":"ad8c8c5ced882df17f7327d580e31cd524660e3ffe1d303d51ba354c08d62aad"}}